带阻尼的非等熵欧拉方程组的爆破

Blowup for the non-isentropic Euler equations with damping

研究带阻尼的非等熵欧拉方程组初边值问题解的爆破现象。利用积分方法证明了当与初始动量有关的加权泛函充分大时,其解将在有限时刻爆破。将近来已知的爆破结果由等熵情形推广到非等熵情形,并在没有绝热常数不大于3的限制下得到了负初始熵情形的爆破结果。

The blowup phenomena of the solutions for the initial-boundary value problem of the non-isentropic Euler equations with damping is studied.It is proved that the solutions will blow up in finite time when a weighed functional associated with the initial momentum is large enough by using the integration method.Some recently known blow-up results are extended from the isentropic case to the non-isentropic case.And the blow-up result for the negative initial entropy case is obtained without the restriction that the adiabatic constant is not bigger than three.